Previous studies on high impedance faults assumed that the erratic behavior of fault current would be random. In this paper we prove that the nature of the high impedance faults is indeed a deterministic chaos not a random motion. Algorithms for estimating Lyapunov spectrum and the largest Lyapunov exponent are applied to various fault currents in order to evaluate the orbital instability peculiar to deterministic chaos dynamically and fractal dimensions of fault currents which represent geometrical self-similarity are calculated. In addition qualitative analysis such a s phase planes Poincare maps obtained from fault currents indicate that the irregular behavior is described by strange attractor.